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TOPCAT - The Theory
by
P.F. Quinn, C.J.M. Hewett and N.D.K. Dayawansa
References
The theory behind the TOPCAT model and some results can also be found in
Quinn, P.F., C.J.M. Hewett and N.D.K. Dayawansa,
'TOPCAT-NP: a minimum information requirement model for simulation
of flow and nutrient transport from agricultural systems,'
Hydrological Processes,
Wiley InterScience, 2008. In Press
interscience.wiley.com
TOPCAT is a simplification of the model TOPMODEL (Quinn and
Beven 1993, Beven et al. 1995) and as such, uses identical soil moisture
stores and subsurface flow equations. TOPCAT does not, however use a topographic
distribution function and thus does not allow the representation of
topographically controlled variable source areas. The model TOPCAT also contains
an extra baseflow/dry weather flow component and two overland flow components
that are caused by intense agricultural management practices.
Figure 1 conceptualises the mechanisms by which a range of hydrological flow paths
deliver nutrients to a channel.
Figure 1 - Hydrological flow paths to channel
The TOPCAT hydrological model (seen in Figure 2), uses a simple
moisture root zone store to receive inputs of rainfall and potential evaporation
per unit time (usually on a daily time step). The moisture content of the root
zone store can fluctuate between SRMIN and SRMAX (which are both
expressed in units of depth). SRMIN is the minimum amount of moisture
retained in the root zone, which represents the permanent wilting point of the
soil. In real terms when the root zone reaches SRMIN the moisture is
empty, hence the actual evaporation falls to zero at this point. SRMAX is
the maximum soil moisture holding capacity of the root zone. SRMAX is a
function of both the soil field capacity and the actual rooting depth of the
vegetation cover. The root zone must be full before any excess rainfall is
allowed to percolate deeper into the soil. This excess percolating flow is
referred to here as Hydrologically Effective Rainfall (HER).
Figure 2 - The TOPCAT Model
Three moisture stores are used in the hydrological model:
the unsaturated zone root zone store, the saturated 'event' subsurface store and
the 'old' subsurface store (or the background flow store). Excess HER is
assumed to move vertically into the subsurface stores within one timestep (i.e.
within one day). A proportion of the HER can bypass the event subsurface
store and enter the old subsurface store. The old subsurface store is
conceptualized as having an infinite storage capacity, thus it will generate a
constant background flow rate (Qback). The parameter SPLIT
controls the fraction of the HER that enters the event subsurface store.
For catchments that are dominated by surface runoff the SPLIT value
should be set to 1 (i.e. 100% of the flow enters the event subsurface store)
and logically the background flow rate should be set to zero. A catchment with a
distinct base flow component requires the value of the background flow rate
Qback to be set as an input parameter, Qback can either be
measured directly during an extended low flow period or can be derived by
calibrating the model.
Conversely, a suitable value of the SPLIT parameter
should be set to reflect the volume of water exiting the catchment as background
flow. The SPLIT parameter can either estimated using a water balance
approach or can be derived by calibrating the model. Quinn et al. (1999)
and Anthony et al. (1996) also conceptualized the background flow to
include 'dry weather flow' which arises from urban sources and sewage treatment
works (which influences the final nutrient estimates).
The rate of subsurface flow leaving the event subsurface
store is approximated to by an exponential function taken directly from TOPMODEL
(Quinn and Beven, 1993; Beven et al., 1995). The current moisture status
in the event subsurface store is described as SBAR which is expressed as
a positive soil moisture deficit value. The rate at which moisture is lost from
the store per unit time is given by:-
where Qb is event sub surface flow and
m is the recession rate parameter. The recession rate parameter can be
approximated by either studying recession rates in observed storm events or from
calibration directly. The term Q0 represents the discharge of
the catchment when the soil moisture deficit is at its lowest and Q0
be determined directly from TOPMODEL theory (Beven et al.,
1995):-
The dimensionless parameter g is
the mean of soils/topographic index and is calculated according to the
expression
where l is the mean of the
TOPMODEL dimensionless topographic index and T0 is the average
transmissivity of the subsurface event store when the soil is just saturated. As
the full version of TOPMODEL is not being used here, a fixed value for l
is used in all applications (the value 7 is used in TOPCAT). l does not affect runoff rates, but only the calculation of
the depth to the water table and thus is only relevant to the full version of
TOPMODEL, not to TOPCAT. However, these terms are left within TOPCAT as the
user may decide to switch to the full version of TOPMODEL at some later date to
investigate further the role of topography and water table depths (Quinn et
al., 1999).
Within each time step the total amount of water in the
subsurface store is determined by calculating the vertical flow entering the
event subsurface store (HER*SPLIT) and the amount leaving (Qb
) :-
where SBAR(t) and
SBAR(t -
1) are the catchment storage deficits at the current and previous
time step respectively.
Quick flow in TOPCAT is assumed to be predominately overland
flow but may include any very fast flow response associated with a surface flow
source. As such, two components of quick flow are represented to reflect intense
agricultural systems and quick flow is always assumed to reach the channel
within one time step. First, the Quick parameter determines the fraction
of rainfall in one time step that converts directly into quick surface runoff.
However, this type of flow is only generated when the root zone reaches field
capacity (SRMAX). This component of quick flow attempts to approximate to
large overland flow 'wash off' events that are commonly observed in intense
arable systems; particularly in winter. As such, it is important to nutrient
losses and erosion wash off (Quinton, 1997). If possible, the Quick
parameter should be calibrated to fit the sharp peaks of runoff observed in
winter drainage periods. In order to reflect agricultural nutrient losses the
value of the Quick parameter should be closely associated with the land
use activity (i.e. for areas with harvested crops or soils with known compaction
problems). In practice the Quick parameter usually lies between 0.05 and
0.3.
The first component of quick flow is:-
where ROQuick (t) is the quick flow
surface runoff, R(t) is rainfall during time step
t.
In order to reflect a key nutrient runoff related flow path,
a second component of overland flow is allowed. This is referred to as the
Critical Source Area (CSA) quick flow. This is based on the observation that,
within intense agricultural zones, some nutrient rich land parcels can be
intersected by active hydrological flow paths that have a direct connection to
the receiving channels. For example, areas close to the channel (including
variable source areas), impermeable roads and their associated ditches, farm
buildings or fields that are cross cut by tyre tracks could all give rise to
quick flow that reaches the channel. Quick CSA runoff can be generated
irrespective of the root zone soil moisture content, and as such can operate in
all storms. Nutrient rich areas close to land drains can be considered as CSAs
as they connect surface overland flow sources of nutrient and sediment directly
to the channels. High losses of phosphate (P), especially sediment attached P,
are carried in preferential flow paths to local field drains and thus to the
channels as reported in Withers et al. (1999). These areas are seen as
small, potent areas of nutrient loss that operate in all storms that give rise
to chronic nutrient pollution problems. A full discussion of CSA concepts can be
found in Preedy et al. (1999), Endriny & Wood (1999), Gburek et
al. (1999), Heathwaite et al. (2000) and Quinn (2002). The inclusion
of the quick CSA flow component, even though it is usually small in magnitude,
can build up to give a significant component of nutrient loss over time. Thus
the quick CSA is estimated using the QuickCSA parameter.
where ROCSA(t) is the runoff
generating from CSAs in each time step and QuickCSA is a fraction
(usually lying between 0 and 1/20).
The two overland flow components work together to reflect
both highly localized features causing chronic pollution and more diffuse
sources of pollution related to acute, large scale quick flow events. Thus, the
model offers an opportunity to investigate the role of these processes in terms
of nutrient pollution management at the catchment scale.
Addition of the quick flow surface runoff and the the runoff
generating from CSAs gives the total surface runoff from the whole catchment:-
where ROTotal(t) is the total
quick flow runoff per unit time.
The total discharge from the catchment is the sum of all the
flow components generated within one timestep:-
where Q(t) is the total stream flow at time
step t. It is the mixing of these flow components that allow a sensible
representation of the nutrient losses to be made at the catchment scale.
Nitrate Transport model TOPCAT-N
The Nitrate component of TOPCAT-N, first estimates
the amount of nitrate (N) leached from the root zone by the HER and then
routes this flow through the event subsurface flow store before it is mixed with
the other flow components in the channel (Figure 2). A significant proportion of
the N that builds up in the soil during the season is assumed to be available to
leaching. The bulk of the leaching is assumed to occur during the main rainy
season i.e. winter, therefore an estimate of the total N available to leaching
before the main drainage period is vital to the model. In Europe, the main
drainage season also occurs just after the main harvest, when nutrients levels
have been raised to their highest. The total amount of N loss is a function of N
available to leaching, the leaching efficiency of the soil and the total amount
of HER.
The N availability (Ninitial) term describes the mass
of N in the root zone prior to the start of the leaching season, at the
beginning of each yearly crop cycle (usually taken as September in Europe). The
value of Ninitial must be obtained either through field sampling or
through existing soil crop N cycle models (Anthony et al., 1996).
Generally, (in European conditions) a surplus of nutrients will build up in
arable soils due to high fertiliser usage and manure application (Owens et
al., 2000; Goulding, 2000). The surplus N undergoes various physical,
chemical and biological changes thus a proportion of this surplus will be
susceptible to leaching. The N available for leaching is determined by the
balance between the applied N and the N in the crop uptake. If the result is a
surplus, then the bulk of this surplus is assumed to be available for leaching .
Figure 3 illustrates the N balance for a typical crop showing the nature of N
available for leaching. Typically the N surplus must be estimated from an
understanding of farming practice within a region assuming that the 'average'
farmer tends to create similar N status of their soil for crop production.
Ninitial is set to a maximum value just before the onset of winter
drainage, thus for multi-year simulations, the value is automatically reset to
this maximum value every 365 days.
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Figure 3
Physically-based models are used to study the primary
nutrient mobilization mechanisms for a wide range of circumstances. This creates
an abundance of output time series that can be analysed and thus mimicked with a
more simple minimum information requirement (MIR) function. In the original
development of TOPCAT (Quinn et al. 1999) developed a simple N loss function
based on the model SLIM (Addiscott and Whitmore, 1991). During the development
of TOPCAT-NP this
work was repeated using the EPIC model (Quinn, 1995).
The EPIC model was chosen as
it contained more N cycling components as well as P and sediment loss estimates.
Figure 4 - N loss from EPIC caused by HER leaching
After many simulations and analyses the EPIC model was seen
to produce a similar outcome to Quinn (1999) where it was concluded that total N
loading was the most important factor, that N leaching was the dominant N loss
mechanism, that a good estimate of total HER was vital and that a direct
relationship existed between N loss pattern and the HER. Figure 4 shows
an example EPIC output run for a 6 year simulation, run at a daily time step,
for a typical UK circumstance (Dayawansa, 2002). The figure also reflects
the fundamental relationship between HER and the estimate of N loss.
Quinn et al. (1999) went on to show that this pattern is produced for a
range of soil types, until a point where the total N in the root zone becomes
depleted.
Figure 5A
Figure 5B
Figure 5C
Figure 5D
Figure 5 illustrates the basic operation of the TOPCAT-N model.
Figure 5A shows the N loss over time, for one drainage season, a fixed soil type (Clay
Loam) and three different Ninitial values (10, 20 and 40 kg/ha). This
reflects the sensitivity of the N loading term. Figure 5B shows a typical time
series of N loss caused by a variation in the soil type (sandy soil, sandy loam
and clay soil) for a fixed Ninitial input. This clearly shows the
sensitivity of the model to soil type. Figure 5C shows how the cumulative N loss
pattern can be captured as a single curve for all soil types if the cumulative
HER is normalized by dividing by the water holding capacity of the soil
(described here as f
). Finally Figure 5D shows that, if the N loss output is converted to a fraction
of the Ninitial term, then a single unique N loss pattern can be
determined for both Ninitial and f.
Thus the N leaching function of TOPCAT-N can be expressed as
e =
HER/f
f = 1.111e -
0.203(e)3 for
e
£ 1.34
f = 1 for e
> 1.34
where f is the cumulative proportion of the original
Ninitial leached. The (HER/f
) term is referred to as the drainage efficiency.
f
is the water holding capacity of the soil and is derived from standard tables
for the soil water holding capacity of a soil type.
f
is usually expressed as a fraction of the water that can be held in 1m of soil
- where in sand it is approximately 0.18 and in clay it is approximately 0.42
(Ministry of Agriculture, Fisheries and Food, 1984).
The N lost within event subsurface flow at any given time
step is given by the difference in the proportion of the N lost between the last
time step and the current time step. This is converted to a concentration by
introducing
Nactive is the amount of N lost in any one time step.
This value is converted to a concentration by knowing the current value of
Qb and converting the units to mg/l.
The model assumes that the N in the quick flow surface runoff
is negligible (0 mg/l). The background N concentration (Nback) is the
concentration of N present in the 'old' subsurface flow (or background flow).
Usually, the background concentrations are reached during the dry periods (the
dry weather flow situation), when there is no influence from recent rainfall
events. Several grab samples of N taken during the extended dry periods should
be sufficient to give a good estimate of the background N concentration. The
'old' N concentration in Qback may reflect both the old denitrified flow
from groundwater sources, urban N sources and effluent from sewage treatment
plants.
The N losses from different flow components combine together
to produce the final stream NO3 concentration. The mixed load
(Lm) is calculated on simple mass balance basis. The mixed
load is divided by total flow to obtain the concentration of N,
CN, in the stream in mg/l.
The P Transport model - TOPCAT-P
The final P concentration found in rivers is based on
mixing a number of flow components together (as seen in Figure 6). Firstly the
concentration of P in old flows (Pback) should be estimated in the field
by direct measurement of the P concentration in low flow periods.
Figure 6 - P Mixing
As with TOPCAT-N, TOPCAT-P is based on mimicking the output of simulations from the
physically based model EPIC and on a number of studies of P dynamics (Sharpley and
Menzel, 1987, Brazier et al., 2001). The situation for P
mobilisation is much more complex than for N, in that P availability is
dependent on the position of the P in the soil profile, and P is susceptible to
attachment to sediment in overland flow. The rate of soluble P loss is also
dependent on the total P loading of the soil and the soil type. Thus, EPIC
simulations were performed to understand the key P loss dynamics and the
functions derived to fit the underlying patterns of P loss.
Figure 7 -
First, in the multiple model simulation of EPIC, the typical
P loss associated with surface flow was determined. In Figure 7, the proportion
of sediment attached P has a simple relationship to both the amount of surface
overland flow and to the sediment loss. Ultimately, this means that a good
estimate of the P available to surface flow and the amount of overland flow are
minimum model requirements. It is also clear from EPIC simulations that one-off
large storms have a significant effect on sediment P loss. Figure 8 shows both
the cumulative total sediment P loss from a 6 year simulation (Dayawansa,
2002) and the P loss after all the large storms have been removed. It is clear
that the many small storms give rise to the 'chronic' P loss pattern and that
there is an acute loss of sediment P in large storms. In hydrological terms
these can be related to QuickCSA flow and Quick parameters
respectively (as outlined in the hydrology section).
Figure 8 -
The EPIC simulations also demonstrated that the total
overland flow was sensitive to the soil type, the local slope and the status of
the soil (i.e. the tillage regime). It is necessary to discern from this
complexity a simple underlying term that allows us to model the sediment P loss.
Hence, it is assumed that only the total amount of overland flow need be
determined for the whole catchment (i.e. the details of the slope, soil type and
tillage status are not used to calculate the overland flow). The amount of
sediment P will be expressed as a function of the amount of total sediment
picked up in overland flow (related to soil type and soil exposure) and the
amount of P that is attached to that sediment (which is a function called the
Enrichment Ratio ER). Thus we require an overland flow generation model
(outlined in the hydrological section), a P distribution term (to state how much
P is in the upper layer of soil (1cm)), the total sediment picked up (per mm of
overland flow) and a term for the ER for each soil type.
The total soil P status determines the overall amount of
surface and sub surface loss of P to the streams (Pinitial). P index
measurement is common in most intense agricultural regions and, as with N
levels, the basic farming regime tends to keep P levels at a suitable level for
crop production. Usually, the total P available to P loss is related to many
chemical reactions present in the soil (Edwards & Withers, 1998).
Extractable inorganic P can be removed from soil by plant uptake, transport in
surface runoff and percolating water, organic P formation and conversion to
forms less readily released to runoff water (Sharpley, 1982). Stratification of
soil P occurs with reduced tillage due to the lack of incorporation of surface
applied fertiliser and manure and from the recycling of subsoil nutrients to the
soil surface by plant growth. Under low tillage conditions, stratification of P
near the surface soil is high (Randall et al., 1998). According
to Sharpley (1982), the amount of P present in the top one cm of soil
is a function of the method and timing of P fertiliser application, soil clay
content and also the P sorption capacity of soil. Accumulation of P
near the soil surface increases the P loss in surface runoff. A highly
significant linear relationship is observed between measured P in surface soil
and the soluble P in runoff (Randall et al., 1998).
In TOPCAT-P, the available soil phosphorus is
considered in two fractions; P in the top one cm soil layer and in the rest of
the root zone. This also reflects the tillage conditions and P availability in
the soil profile and also the degree of stratification of available P. Available
P in the top one-cm layer is calculated as a fraction of total available P in
the whole root zone. In many agricultural areas, soil P status exceeds crop
needs and hence enriches surface runoff (Sharpley et al., 2000). Thus
management of P in the soil profile is an important control for the reduction of
sediment attached P.
The TOPCAT-P model assumes that the highest residual/surplus
P is available for loss at the end of the harvest which is identical to the
TOPCAT-N yearly cycling.
Soluble P concentration in surface runoff depends on the
amount of water extractable P in the top one cm soil layer prior to rainfall
(Sharpley, 1982). The movement of dissolved P begins with the re-sorption,
dissolution, and extraction of P from the soil, plant, and organic material.
These processes occur when surface water interacts with the thin layer of
surface soil (USDANRCS, 1994). The total available P in the root zone and in
the top 1cm of soil is shared between these two soil layers using a P
Distribution Coefficient (PDC). Phosphorus in the first one cm of the
soil is calculated as
Where PTOP(t) is the available P in
first 1cm of the soil layer and Pinitial is the total P in the root zone
of the soil.
This PDC coefficient has the freedom to adjust the P
positioning in the soil according to the tillage regime and other land
management practices. Stratification of P towards the surface layer of soil is
observed in agricultural soils due to low incorporation of frequently applied
fertiliser and manure in the sub soil. This again reflects the role that a
number of land management options have on the degree of P transport.
Soluble P loss in the surface runoff on the initial day of
simulation is calculated using the same formula used in EPIC (Williams, 1995)
and AGNPS (Young et al., 1995). This is proportional to the available P
in the top one cm of soil and the amount of surface runoff (ROTotal). We
have
Where PSOL(t) is the soluble P in
runoff in kg/m2 on day t and K is the extraction
coefficient used to partition P between sediment and solution.
The tendency of a chemical species to sorb to sediment is
called partitioning (Logan, 1995). Partitioning is an equilibrium process where
the extent of partitioning is expressed by an extraction coefficient K
set to 1/175; which is the value used in the EPIC water quality model. Soluble P
loss is estimated at each time step by depleting the P reserve in the top one
cm of soil by the amount lost in that time step. The soluble P loss in one time
step is related to the total P remaining in the top 1cm of soil and the overland
flow:-
where PSOL(t+1) is the soluble P
transport in the next time step of the simulation in kg/m2,
PRES(t) is the P reserve in the soil.
Depletion of the P reserve is updated daily by subtracting
the daily losses of soluble P and sediment P.
P in the rest of the soil profile available for sub surface
losses is also updated on the same manner. The ultimate concentration of
soluble P transport in surface runoff, CPHOS , is obtained in
mg/l according to;
The loss of sediment attached P is based on: the quantity of
sediment eroded, the amount of surface runoff and also the Enrichment Ratio
(ER) of P to sediment particles.
Soil erosion is a function of rainfall characteristics, soil
texture, topography of the landscape, crop and land management practices. As
soil erosion is a selective process, the sediment attached P also shows
selectivity (Sharpley, 1980). Sharpley found that enrichment occurs only with
finer particles of diameter less than 20mm. One
result of this process is that the eroded soil is richer in P than the source
soil. This is expressed by the Enrichment Ratio, ER. To quantify the
sediment attached fraction of P, it is important to evaluate the amount of
sediment generated under a given land use and the current soil conditions
(tilled or not tilled).
The MIRSED model of Brazier et al. (2001) produced a
matrix of sediment transport rates expressed as kg / 1 mm of quick flow/metre
width of hillslope for various land use and soil conditions in the UK. Sediment
P values in TOPCAT are calculated using these MIRSED values. Hence
Where; SED(d)(t) is the sediment discharge
and SED(l)(t) is the sediment loss/unit depth of quick
flow/unit width of hillslope. The value of SED(l)(t) is
obtained using the results reported in Brazier et al. (2001). Brazier
has run the WEPP model, a physically-based model for many combinations of soil
textures, land use conditions and slopes to identify key sediment transport
patterns. This enabled relationships to be determined between soil loss and soil
texture, for a number of land uses over a 30 year simulation period. The MIRSED
model was developed following the full MIR modelling process and thus the
sediment erosion values determined reflect the key parameters affecting
potential sediment loss from UK soils. A 3D matrix has been derived showing the
erosion rates expressed as soil loss/mm of quick flow/metre width of hillslope.
The axes of the matrix are soil type (expressed as the fraction of clay in the
soil), the crop under cultivation and the local slope. As the slope term is
related to the total overland flow production only, this can be replaced by the
quick flow hydrological component. Thus, according to the erosion matrix, the
soil type and cropping activities are the main controls of sediment transport.
As an example Brazier et al. (2001) performed two simulations, where only the
crop type was changed. The results revealed that the erosion loss rate was 0.3
kg/mm/m for an arable crop and only 0.0006 kg/mm/m for permanent pasture. Under
most circumstances the arable crop value is used in TOPCAT as it reflects
intense agriculture systems prone to wash off events.
When the amount of P applied to the soil increases, it
results in a dramatic increase in ER for P.
Menzel (1980)
has obtained a
significant relationship between ER and the sediment concentration after
working with several soils with varying physical and chemical properties, slope,
rainfall intensity and P sources. This relationship is linear when the
logarithm of ER is plotted against the logarithm of sediment
concentration for each individual runoff events. For all soils, if the amount of
P added to the soils increases then there is a marked increase in ER. The
general relationship obtained in that study was
where ER is the P enrichment ratio and
SED(d ) is the daily sediment delivery in kg/ha.
The Menzel equation was incorporated into TOPCAT-P and used
in the following equation to calculate the sediment P transport.
Where PSED(t) is the quantity of
sediment attached P and SBD is the effective soil bulk density.
SBD should vary as other soil parameters vary. For example if f
is set to the value for clay then the soil
bulk density should change accordingly. The parameter is an effective parameter
that roughly reflects the shear strength of the soil.
The total P remaining in the top 1cm of soil is now updated:-
Finally, the runoff sediment P concentration,
CPSED, is calculated using
Note that both overland flow mechanisms are treated together,
i.e. it is the total estimate of overland that is used in the estimation of
soluble and sediment P loss in surface flows.
Many studies have confirmed that subsurface hydrological
pathways also play a substantial role in removing soil P to stream water under
certain conditions (Preedy et al., 1999; Hesketh and Brookes, 2000;
Schoumans and Groenendijk, 2000). Excess application of P over a long period is
accumulated near surface or subsoil horizons. Most of this P is fixed by the
soil. However, when the soil profile is saturated with P, a greater proportion
is transported to surface waters through subsurface pathways (Sims et
al., 2000). Hesketh and Brookes (2000) estimated a threshold level of
around 60 mg Olsen P/kg of soil is a critical concentration at which leaching
starts for all soils, then the risk of P leaching from soil to water will be
small. Hesketh and Brookes estimated that only about 20 percent of the UK soils
are at the saturated P level or and therefore the remaining 80% are at less risk
of contaminating water. Working in Northern Ireland, Jordan et al. (2000)
found a similar
threshold at only 22 kg/ha for highly compacted pasture land. These findings
justify the importance of a subsurface soluble P loss component. Subsurface P
removal is calculated with the same basic empirical leaching equation used in
TOPCAT-N. This equation should be adjusted to accommodate the sorption and de-
sorption occurring within the profile when the P is moving through the profile.
This equation is more suitable for application to nutrient rich soils with high
Olsen P levels.
 for e
£
1.34
 for
e
> 1.34
PSUB(t) is the fraction of P leached
and AD is the adsorption/desorption coefficient for the soil. The value
of AD coefficient is set to 0.1 assuming that 90% of the leaching P is
re- adsorbed by the soil when passes through the profile. However, this may
take a larger value for the older soils with a long history of agricultural
activity and P loading. Therefore, long term loading of P is reflected with a
higher AD value and the land management factor can then be demonstrated
to the end user. The AD value ensures that the amount of P available to
leaching is much lower that the total P but that other components of the total P
could be available to surface runoff due to cultivation practice. AD is
best left as a constant value in the model as there are a number of other, more
powerful P parameters (such as Pinitial) that can be used to create the
final soluble P concentration in the stream.
The mixed load is calculated with three different P loss
types and their corresponding flow values.
where PSOLLOAD(t) is the mixed
soluble P load, PSUB(t) is the P in percolate,
PBACK(t) is the P in the background flow.
The total P load in the stream,
PLOAD(t), is given by
The stream soluble P concentration, CPSOL,
in the stream is evaluated using
where CPSOL is measured in mg/l.
The stream total P concentration, CPTotal,
is calculated using
P.F. Quinn, C.J.M. Hewett and N.D.K. Dayawansa
March, 2003
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